Simplified method to nonlinear analysis of reinforced concrete in pure flexure
Date
2015-03-22
Authors
Roberts, Graham Dean
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The use of the finite element method in the design of reinforced concrete slabs and beams has
become a generally accepted practice in recent times and when designing structural members,
both ultimate and serviceability limit states are required to be considered in the consequent
analyses. The nonlinear analysis of reinforced concrete, using plates and shells, may be
defined into two broader categories with the first being the layered approach and the second
being the effective stiffness approach.
Common commercial finite element software do not all provide the facilities for the nonlinear
analysis of reinforced concrete beams and slabs. Although there are currently nonlinear
models provided through literature these can be seen as complex to certain engineers and
only applicable to the specialist engineer able to understand and implement the theory
correctly.
The more complex methods are also aimed at predicting the wider range of failure
mechanisms. Unless carrying out forensic engineering, the design engineer might not be
interested in the actual failure load but rather, dependant on design philosophy, a cautious
yield line load or similar.
This report presents a simplified method, based on an effective stiffness approach, to the
nonlinear analysis of reinforced concrete slabs and beams for serviceability and ultimate limit
states. The method allows for the use of simple design equations familiar to all structural
engineers undertaking reinforced concrete designs. Using the finite element method, plate elements and simplified constitutive properties a
nonlinear algorithm is developed which results in the accurate estimation of the displacements
during loading as well as a design ultimate loading. The proposed method is intended for
reinforced concrete beams and slabs under transverse loading leading to bending with no axial
forces present.
The proposed model and nonlinear algorithm is validated against four experimental case
studies which show the accuracy and relevance of the given nonlinear solution. The results
provide evidence that the proposed nonlinear model is valid for all loading and boundary
conditions considered. The application can be for displacement serviceability checks or the
ultimate load design of a slab or beam. The nonlinear model and algorithm presented can be
easily integrated into a commercial finite element package, with API capabilities, for use in the
design of reinforced concrete slabs and beams.